I know about that, the Task Manager. I do that regularly. End all my running applications...
You shouldn't do this, it will make matters worse.
Your phone will use more power restarting applications you have closed than you will ever save by killing them. It's a long time since this has been a good idea and task killers have bitten the dust for this reason.
Is this always always always true?
I ask because I had a theory that stupid Candy Crush Saga was sucking my battery dry, as I've seen a vast change in battery draining behavior over the past week, which coincided with my use of said app.
I googled the theory, and discovered this
Verizon Support page, which lists some apps that suck the life out of your battery. It includes Candy Crush Saga and, as it happens, Asphalt 7, which was named by the OP as a possible culprit as well. Verizon says that both of these apps, when left running, will "keep the device from going into sleep mode" and that, if you leave the device untouched with the app running, the battery will drain 2.6 (Candy Crush) or 2.7 (Asphalt 7) times faster than normal. VZW recommends closing the game when done playing.
I also read -- although I can't recall where -- something strongly suggesting that developers should stop releasing apps that do this, and that the public won't stand for what is basically a flaw in their coding. Which I interpreted to mean: OK, yes, generally you shouldn't use a task manager because Android is designed to properly allocate resources among running apps, but
sometimes you should close stuff yourself when the people making your apps did not design them to run properly in an Android environment.
FWIW, I started closing out Candy Crush via Task Manager -- it's only been a day, but my battery life appears to have returned to normal.